For reasons given in the discussion at the beginning of this section, we list only results from 1989 and later. $\langle{}\lambda \rangle{}$ = $\lambda \mathit U_{{{\mathit e}} \mathit j}\mathit V_{{{\mathit e}} \mathit j}$ and $\langle{}\eta \rangle{}$ = ${{\mathit \eta}}$ $\mathit U_{{{\mathit e}} \mathit j}\mathit V_{{{\mathit e}} \mathit j}$, where the sum is over the number of neutrino generations. This sum vanishes for massless or unmixed neutrinos. In the following Listings, only best or comparable limits or lifetimes for each isotope are reported.

$\langle{}\lambda \rangle{}$ ($10^{-6}$) CL$\%$ $\langle{}\eta \rangle{}$ ($10^{-8}$) CL$\%$ ISOTOPE METHOD DOCUMENT ID • • We do not use the following data for averages, fits, limits, etc. • • $ \text{< 2.2 - 2.6} $ 90 $<$ $1.7 - 2.1$ 90 ${}^{82}\mathrm {Se}$ NEMO-3 1 ARNOLD 2018 $ \text{< 1.8 - 22} $ 90 $<$ $1.6 - 21$ 90 ${}^{116}\mathrm {Cd}$ AURORA 2 BARABASH 2018 $ \text{<0.9 - 1.3} $ 90 $<0.5 - 0.8$ 90 ${}^{100}\mathrm {Mo}$ NEMO-3 3 ARNOLD 2014 $ <120 $ 90 ${}^{100}\mathrm {Mo}$ $0{}^{+} \rightarrow 2{}^{+}$ 4 ARNOLD 2007 $ 0.692 {}^{+0.058}_{-0.056} $ 68 $0.305$ ${}^{+0.026}_{-0.025}$ 68 ${}^{76}\mathrm {Ge}$ Enriched ${}^{}\mathrm {HPGe}$ 5 KLAPDOR-KLEIN.. 2006 A $ <2.5 $ 90 ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}$ , NEMO-3 6 ARNOLD 2005 A $ <3.8 $ 90 ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}$ , NEMO-3 7 ARNOLD 2005 A $ \text{<1.5 - 2.0} $ 90 ${}^{100}\mathrm {Mo}$ 0${{\mathit \nu}}$ , NEMO-3 8 ARNOLD 2004 $ \text{< 3.2 - 3.8} $ 90 ${}^{82}\mathrm {Se}$ 0${{\mathit \nu}}$ , NEMO-3 9 ARNOLD 2004 $ \text{<1.6 - 2.4} $ 90 $<0.9 - 5.3$ 90 ${}^{130}\mathrm {Te}$ Cryog. det. 10 ARNABOLDI 2003 $ <2.2 $ 90 <2.5 90 ${}^{116}\mathrm {Cd}$ ${}^{116}\mathrm {Cd}WO_{4}$ scint. 11 DANEVICH 2003 $ \text{<3.2 - 4.7} $ 90 $<2.4 - 2.7$ 90 ${}^{100}\mathrm {Mo}$ ELEGANT V 12 EJIRI 2001 $ <1.1 $ 90 <0.64 90 ${}^{76}\mathrm {Ge}$ Enriched HPGe 13 GUENTHER 1997 $ <4.4 $ 90 <2.3 90 ${}^{136}\mathrm {Xe}$ TPC 14 VUILLEUMIER 1993 $ $ <5.3 ${}^{128}\mathrm {Te}$ Geochem 15 BERNATOWICZ 1992 1  ARNOLD 2018 use the NEMO03 tracking detector, with 0.93 kg of ${}^{82}\mathrm {Se}$ mass and 5.25 y exposure to obtain the limits for the hypothetical right-handed currents. Supersedes ARNOLD 2005A. 2  BARABASH 2018 use 1.162 kg of ${}^{116}\mathrm {Cd}WO_{4}$ scintillating crystals to obtain this limits for the hypothetical right-handed currents in the 0 ${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ decay of ${}^{116}\mathrm {Cd}$. 3  ARNOLD 2014 is based on 34.7 kg yr of exposure of the NEMO-3 tracking calorimeter. The reported range limit on $\langle \lambda \rangle $ and $\langle \eta \rangle $ reflects the nuclear matrix element uncertainty in ${}^{100}\mathrm {Mo}$. 4  ARNOLD 2007 use NEMO-3 half life limit for 0${{\mathit \nu}}$ -decay of ${}^{100}\mathrm {Mo}$ to the first excited 2${}^{+}$-state of daughter nucleus to limit the right-right handed admixture of weak currents $\langle \lambda \rangle $. This limit is not competitive when compared to the decay to the ground state. 5  Re-analysis of data originally published in KLAPDOR-KLEINGROTHAUS 2004A. Modified pulse shape analysis leads the authors to claim 6$\sigma $ statistical evidence for observation of 0${{\mathit \nu}}$ -decay. Authors use matrix element of MUTO 1989 to determine $\langle \lambda \rangle $ and $\langle \eta \rangle $. Uncertainty of nuclear matrix element is not reflected in stated errors. 6  ARNOLD 2005A derive limit for $\langle {{\mathit \lambda}}$ $\rangle $ based on ${}^{100}\mathrm {Mo}$ data collected with NEMO-3 detector. No limit for $\langle {{\mathit \eta}}$ $\rangle $ is given. Supersedes ARNOLD 2004 . 7  ARNOLD 2005A derive limit for $\langle {{\mathit \lambda}}$ $\rangle $ based on ${}^{82}\mathrm {Se}$ data collected with NEMO-3 detector. No limit for $\langle {{\mathit \eta}}$ $\rangle $ is given. Supersedes ARNOLD 2004 . 8  ARNOLD 2004 use the matrix elements of SUHONEN 1994 to obtain a limit for $\langle {{\mathit \lambda}}$ $\rangle $, no limit for $\langle {{\mathit \eta}}$ $\rangle $ is given. This limit is more stringent than the limit in EJIRI 2001 for the same nucleus. 9  ARNOLD 2004 use the matrix elements of TOMODA 1991 and SUHONEN 1991 to obtain a limit for $\langle {{\mathit \lambda}}$ $\rangle $, no limit for $\langle {{\mathit \eta}}$ $\rangle $ is given. 10  Supersedes ALESSANDRELLO 2000 . Cryogenic calorimeter search. Reported a range reflecting uncertainty in nuclear matrix element calculations. 11  Limits for $\langle {{\mathit \lambda}}$ $\rangle $ and $\langle {{\mathit \eta}}$ $\rangle $ are based on nuclear matrix elements of STAUDT 1990 . Supersedes DANEVICH 2000 . 12  The range of the reported $\langle {{\mathit \lambda}}$ $\rangle $ and $\langle {{\mathit \eta}}$ $\rangle $ values reflects the spread of the nuclear matrix elements. On axis value assuming $\langle {\mathit m}_{{{\mathit \nu}}}\rangle $=0 and $\langle {{\mathit \lambda}}$ $\rangle =\langle {{\mathit \eta}}$ $\rangle $=0, respectively. 13  GUENTHER 1997 limits use the matrix elements of STAUDT 1990 . Supersedes BALYSH 1995 and BALYSH 1992 . 14  VUILLEUMIER 1993 uses the matrix elements of MUTO 1989 . Based on a half-life limit $2.6 \times 10^{23}~$y at 90$\%$CL. 15  BERNATOWICZ 1992 takes the measured geochemical decay width as a limit on the 0${{\mathit \nu}}$ width, and uses the SUHONEN 1991 coefficients to obtain the least restrictive limit on ${{\mathit \eta}}$ . Further details of the experiment are given in BERNATOWICZ 1993 .

References:

ARNOLD 2018 EPJ C78 821 Final results on ${}^\mathbf 82 \hbox {Se}$ double beta decay to the ground state of ${}^\mathbf 82 \hbox {Kr}$ from the NEMO-3 experiment BARABASH 2018 PR D98 092007 Final results of the Aurora experiment to study $2\beta$ decay of $^{116}\mathrm{Cd}$ with enriched $^{116}\mathrm{Cd}{\mathrm{WO}}_{4}$ crystal scintillators ARNOLD 2014 PR D89 111101 Search for Neutrinoless Double-beta Decay of ${}^{100}\mathrm {Mo}$ with the NEMO-3 Detector ARNOLD 2007 NP A781 209 Measurement of Double beta Decay of ${}^{100}\mathrm {Mo}$ to Excited States in the NEMO-3 Experiment KLAPDOR-KLEINGROTHAUS 2006A MPL A21 1547 The Evidence for the Observation of 0 ${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ Decay: the Identification of 0 ${{\mathit \nu}}{{\mathit \beta}}{{\mathit \beta}}$ Events from the Full Spectra ARNOLD 2005A PRL 95 182302 First Results of the Search for Neutrinoless Double-Beta Decay with the NEMO 3 Detector ARNOLD 2004 JETPL 80 377 Study of 2${{\mathit \beta}}$ Decay of ${}^{100}\mathrm {Mo}$ and ${}^{82}\mathrm {Se}$ using the NEMO3 Detector ARNABOLDI 2003 PL B557 167 A Calorimetric Search on Double beta Decay of ${}^{130}\mathrm {Te}$ DANEVICH 2003 PR C68 035501 Search for 2$\beta $ Decay of Cadmium and Tungsten Isotopes: Final Results of the Solotvina Experiment EJIRI 2001 PR C63 065501 Limits on the Majorana Neutrino Mass and Right-Handed Weak Currents by Neutrinoless Double $\beta $ Decay of ${}^{100}\mathrm {Mo}$ GUENTHER 1997 PR D55 54 Heidelberg Moscow $\beta $ $\beta $ Experiment with ${}^{76}\mathrm {Ge}$: Full Setup with Five Detectors VUILLEUMIER 1993 PR D48 1009 Search for Neutrinoless Double $\beta $ Decay in ${}^{136}\mathrm {Xe}$ with a Time Projection Chamber BERNATOWICZ 1992 PRL 69 2341 Neutrino Mass Limits from a Precise Determination of $\beta $ $\beta $ Decay Rates of ${}^{128}\mathrm {Te}$ and ${}^{130}\mathrm {Te}$